The SI unit of electrical conductivity is the siemens per metre (S/m). The SI unit of electrical conductance is the siemens (S). The two are easy to mix up: conductance belongs to a particular wire or component, while conductivity is a property of the material itself, so it carries the extra “per metre”.
One siemens equals one reciprocal ohm (1 S = 1 Ω⁻¹). Older books call this unit the mho (ohm spelt backwards) and write it as ℧, so you will also see conductivity written as mho/m or Ω⁻¹ m⁻¹.
Conductance vs conductivity at a glance
| Quantity | Symbol | Formula | SI unit | Depends on shape? |
|---|---|---|---|---|
| Resistance | R | R = V / I | ohm (Ω) | Yes |
| Conductance | G | G = 1 / R | siemens (S) | Yes |
| Resistivity | ρ | ρ = R A / L | ohm metre (Ω·m) | No, material property |
| Conductivity | σ (or κ in chemistry) | σ = 1 / ρ | siemens per metre (S/m) | No, material property |
| Molar conductivity | Λₘ | Λₘ = κ / c | S·m²·mol⁻¹ | Used for electrolytes |
Where the unit S/m comes from
Start from the resistance of a uniform wire: R = ρ L / A, where L is length and A is cross-sectional area. Rearranging gives resistivity ρ = R A / L, with units Ω × m² / m = Ω·m. Conductivity is the reciprocal of resistivity:
σ = 1 / ρ = L / (R A)
So its unit is 1 / (Ω·m) = Ω⁻¹ m⁻¹ = S/m. Written in SI base units this is kg⁻¹ m⁻³ s³ A², and the dimensional formula is [M⁻¹ L⁻³ T³ A²].
Conductance works the same way for a single component: G = 1 / R, so its unit is Ω⁻¹, which is the siemens.
Typical conductivity values
| Material (about 20 °C) | Conductivity σ (S/m) |
|---|---|
| Silver | 6.3 × 10⁷ |
| Copper | 5.96 × 10⁷ |
| Aluminium | 3.5 × 10⁷ |
| Seawater | about 5 |
| Drinking water | 0.005 to 0.05 |
| Pure (deionised) water | about 5.5 × 10⁻⁶ |
| Glass | 10⁻¹¹ to 10⁻¹⁵ |
Water quality meters usually report conductivity in µS/cm or mS/cm rather than S/m, because the numbers are more convenient. The conversion is 1 S/m = 10,000 µS/cm = 10 mS/cm.
Solved examples
1. Conductance of a resistor. A resistor has R = 25 Ω. Its conductance is G = 1 / 25 = 0.04 S (40 mS).
2. Conductivity of a wire. A wire 2 m long with cross-section 1 mm² (1 × 10⁻⁶ m²) has a resistance of 0.034 Ω. Its conductivity is σ = L / (R A) = 2 / (0.034 × 1 × 10⁻⁶) = 5.9 × 10⁷ S/m. That value matches copper.
3. Converting a water meter reading. A meter shows 500 µS/cm. In SI units that is 500 ÷ 10,000 = 0.05 S/m.
Don’t confuse it with thermal conductivity
Thermal conductivity (k) measures how well a material conducts heat, not electric current. Its SI unit is the watt per metre kelvin, W/(m·K). Copper, for example, has a thermal conductivity of about 400 W/(m·K). If a question mentions heat flow or temperature gradient, it wants this unit, not S/m.
Frequently asked questions
What is the SI unit of conductance?
The SI unit of electrical conductance is the siemens (S), which equals one reciprocal ohm (Ω⁻¹). The older name is mho.
What is the SI unit of electrical conductivity?
Electrical conductivity is measured in siemens per metre (S/m), which can also be written Ω⁻¹ m⁻¹ or mho per metre.
Is mho the same as siemens?
Yes. One mho equals one siemens. Siemens is the official SI name; mho is an older name still seen in some Indian textbooks.
What is the dimensional formula of conductivity?
The dimensional formula of electrical conductivity is [M⁻¹ L⁻³ T³ A²].
What is the unit of molar conductivity?
Molar conductivity of an electrolyte is measured in S·m²·mol⁻¹; in chemistry books it often appears as S·cm²·mol⁻¹.
References
- NIST – SI Units
- NCERT Class 12 Physics, Chapter 3 “Current Electricity” and Class 12 Chemistry, Chapter 2 “Electrochemistry”.